ETCHING OF CRYSTALS THEORY, EXPERIMENT, AND APPLICATION

Keshra SANGWAL

Institute of Physics Technical University of Lodz Wolczanska 219, 93005 Lodz POLAND

1987

NORTH-HOLLAND AMSTERDAM • OXFORD • NEW YORK • TOKYO

CONTENTS

Preface vii

1. Defects in crystals 1 1.1. Nature of crystal surfaces 1 1.2. Point defects and their clusters 2 1.3. Dislocations 4

1.3.1. Edge dislocations 4 1.3.2. Screw dislocations 5 1.3.3. Edge dislocations intersecting the {111} surface of

III-V compounds 6 1.3.4. Burgers vector of a dislocation 8 1.3.5. Energy associated with dislocations 9 1.3.6. Slip and climb of dislocations 12

1.4. Boundaries between regions of different orientations 13 1.5. p-n homojunctions and double heterojunctions 14 1.6. Growth striatums, sector boundaries and lineages 16

2. Detection of defects 18 2.1. Growth spirals 18 2.2. Chemical etching 20

2.2.1. Chemical etch pits 20 2.2.2. Chemical etch spirals 20 2.2.3. Etch hillocks 22 2.2.4. Electrolytic etching 23

2.3. Thermal etching 24 2.4. Preferential oxidation 26 2.5. Preferential dehydration and decomposition 26

Contents

2.6. Ion-bombardment etching 27 2.7. Enhanced nonradiative recombination techniques 27 2.8. Decoration techniques 31 2.9. Topographic techniques 32 2.10. The photoelastic method 35 2.11. Thin-film techniques 37 2.12. Advantages and limitations of the different methods to study

defects 39

Growth and dissolution of crystals 43 3.1. Conditions of the formation of growth nuclei 43 3.2. Nucleation 44

3.2.1. Homogeneous nucleation 44 3.2.2. Heterogeneous nucleation 47

3.3. Kinetics of crystal growth 49 3.3.1. Rate of formation of critically sized two-dimensional

nuclei 50 3.3.2. The normal growth rate according to two-dimensional

theories 51 3.3.3. The surface diffusion growth theory of Burton, Cabrera

and Frank 53 3.3.4. Bulk diffusion theories 55 3.3.5. Equations of steady-state velocity of a parallel train of

ledges 56 3.4. Surface entropy factor 58

3.4.1. Surface roughening and the a-factor 58 3.4.2. Estimation of the a-factor 61

3.5. The morphology of crystals 62 3.5.1. The Gibbs-Wulff theorem for equilibrium forms 63 3.5.2. The approach of Stranski and Kaischew 66 3.5.3. Periodic bond chains (PBCs) 67

3.6. Growth forms from the viewpoint of growth kinetics 69 3.7. Effect of impurities on kinetics and growth form 71 3.8. Ordered impurity-adsorption layers and growth morpho-

dromes 75 3.9. Growth controlled by mass and heat transfer 79 3.10. Growth controlled by simultaneous mass transfer and surface

reactions 81 3.11. Reciprocity of growth and dissolution 82 3.12. Surface roughening during diffusion-controlled dissolution 84 3.13. Crystal-solution interfacial layer 84

Contents xv

3.14. Anisotropy of the macroscopic dissolution rate 85

4. Theories of dissolution and etch-pit formation 87 4.1. The nature of pit sites 88 4.2. Kinematic theories 88

4.2.1. Geometric-kinetic theories and stability criteria for hillocks and pits 88

4.2.2. The kinematic theory of step motion 91 4.2.2.1. Kinematic waves and their trajectories 91 4.2.2.2. Formation of shock waves 96 4.2.2.3. Application of kinematic waves to dissolution

and dislocation etch-pit profiles 104 4.2.2.4. Equilibrium and crystallographic pits 106 4.2.2.5. A phenomenological model for the dislocation

etch-pit slope 112 4.2.3. Molecular-kinetic theories of dissolution 114

4.3. Thermodynamic theories 119 4.3.1. The nucleation process at a perfect surface 121 4.3.2. The formation of a two-dimensional nucleus at a

dislocation site 122 4.3.2.1. Cabrera's theory 122 4.3.2.2. Criticism of Cabrera's theory 125 4.3.2.3. Schaarwächter's theory 126 4.3.2.4. Other thermodynamic models 127

4.3.3. The formation of visible etch pits 136 4.3.3.1. Theoretical aspects 136 4.3.3.2. Some experimental results 140

4.4. Diffusion theories 146 4.4.1. Vermilyea's interfacial-layer theory of macroscopic

dissolution of ionic crystals 147 4.4.2. Böhm and Kleber's diffusion theory of etch-pit for­

mation 149 4.4.3. The mechanism of inhibitor diffusion for etch-pit for­

mation 150 4.5. Topochemical adsorption theories 156

4.5.1. Kleber's adsorption theory 156 4.5.2. Other models 158

4.6. The present-day situation 158

5. Chemical aspects of the dissolution process 161 5.1. Catalytic reactions 161

XVI Contents

5.2. Elementary steps involved in dissolution 162 5.3. Types of reactions during dissolution 163 5.4. Formation of oxide layers 164 5.5. Dissolution of water-soluble crystals 167 5.6. Dissolution of water-insoluble ionic crystals 170 5.7. Dissolution of metals 176 5.8. Dissolution of semiconductors 181

5.8.1. Carrier-limited kinetics 181 5.8.2. Surface-reaction mechanisms 184

5.9. Maxima in the curves of dissolution rate versus etchant com­position 189

5.10. Relation between etch rate and the pH of the solution 193

6. Solubihty of crystals and complexes in solution 196 6.1. The structure of solvents and solutions 196 6.2. Solvation and solubility 199 6.3. Solvents for crystals and estimation of crystal solubihty in

solvents other than water 202 6.4. Temperature dependence of the solubihty 205 6.5. The relationship between solubihty, surface energy and hard­

ness of crystals 207 6.6. Complexes in solution and their structure 210 6.7. Stability of complexes 216 6.8. Size and charge of complexes 217

7. The kinetics and the mechanism of dissolution: a survey of experi­mental results 218 7.1. Alkali halide crystals 219

7.1.1. Effect of added salts and their concentration 219 7.1.2. Effect of undersaturation and addition of water, acids

and organic liquids 222 7.1.3. Effect of solvent and crystallographic orientation 224 7.1.4. Relation between concentration of additives and crys­

tal solubihty 226 7.1.5. Effect of etching time 227 7.1.6. Influence of stirring 228 7.1.7. Effect of temperature 229

7.2. Other water-soluble dielectrics and insulators 230 7.2.1. Effect of solvent and crystallographic orientation 230 7.2.2. Effect of addition of acids and inorganic salts 231 7.2.3. Effect of temperature and stirring 231

Contents xvu

7.3. Water-insoluble dielectrics and insulators 231 7.3.1. Etching in aqueous solutions of acids, acidic salts and

alkalies 231 7.3.2. Etching in molten salts and alkalies 235 7.3.3. Hydrothermal etching 235 7.3.4. Effect of crystallographic orientation 235 7.3.5. Effect of etching time 236 7.3.6. Effect of temperature and addition of viscous liquids 238

7.4. Metallic crystals 243 7.4.1. Etching in acids and acidic salts 243 7.4.2. Etching in halogens and other oxidizing reagents 244 7.4.3. Etching in aqueous solutions of alkalies 245 7.4.4. Etching in solutions of salts 245 7.4.5. Effect of the etching medium 247 7.4.6. Effect of inhibitors and etching time 249 7.4.7. Effect of crystallographic orientation 250

7.5. Semiconductors 251 7.5.1. Etching in aqueous solutions of acids, alkalies and

salts 251 7.5.2. Effect of impurities on etch rates and dislocation etch-

pit formation 255 7.5.3. Etching in molten salts and alkalies 257 7.5.4. Influence of temperature 259 7.5.5. Surface orientation effects 261 7.5.6. Effect of illumination 263

Some typical observations on etch pits and the morphology of etched surfaces 265 8.1. Etch pits at fresh and aged dislocations 265 8.2. Distinction between edge and screw dislocations 269 8.3. Positive and negative dislocations 272 8.4. Etch pits associated with dislocations with different Burgers

vector 273 8.5. Effect of the inclination of dislocations on the morphology and

size of etch pits 274 8.6. Formation of beaks and etch tunnels 278 8.7. Branching and bending of dislocations 279 8.8. Solution channels, dislocation loops and networks 280 8.9. Helical dislocations 281 8.10. Star-shaped chemical etch pits 282 8.11. Etch pits at clusters of vacancies and impurities 283

XV111 Contents

8.12. Formation of etch hillocks by gas bubbles 284 8.13. Morphology of etched surfaces and terracing of dislocation

pits 289 8.13.1. Origin of bunches 289 8.13.2. Observed micromorphology of etched surfaces 292 8.13.3. Terracing of dislocation etch pits 295 8.13.4. Formation of block patterns 299

9. Morphology of etch pits 302 9.1. Factors affecting etch-pit morphology 302 9.2. Etch-pit morphology according to Ives 306 9.3. Analysis of the outline of etch pits by considering the crystal

structure 310 9.3.1. Etch-pit geometry deduced from the atomic arrange­

ment 311 9.3.1.1. NaCl-type lattice 311 9.3.1.2. CsCl-type lattice 312

9.3.2. Etch-pit geometry from PBC vectors 313 9.3.2.1. NaCl-type lattice 313 9.3.2.2. CsCl-type lattice 313 9.3.2.3. Fluorite-type lattice 313 9.3.2.4. fee metals 316

9.3.3. Shape of etch pits on matched cleavages 317 9.3.4. Simulation of pit morphologies 318

9.4. Inhibition of dissolution steps by poisons and reaction pro­ducts 325 9.4.1. Possible centres for inhibition on cube faces of a halite-

type lattice 325 9.4.2. Inhibiting species and inhibition at T-L-K sites in

alkali halides 331 9.4.3. Inhibition in water-insoluble crystals 334 9.4.4. Formation of circular etch pits 335 9.4.5. Relation between J-p curves and etch-pit geometry 336

9.5. Effect of optically active substances on pit morphology 337 9.6. Effect of some other factors on etch-pit morphology 339 9.7. Stability of complexes and formation of etch pits 339

10. Selection of dislocation etchants and polishing solutions 343 10.1. Dielectrics and insulators 343

10.1.1. Water-soluble crystals 343 10.1.2. Water-insoluble crystals 351

Contents xix

10.1.3. Guidelines for choosing the etchant composition for dielectrics and insulators 351

10.2. Metallic and semiconductor crystals 353 10.2.1. Metallic crystals 353 10.2.2. Semiconductors 356 10.2.3. Guidelines for choosing dislocation etchants for metals

and semiconductors 359 10.3. Surface polishing 360 10.4. Reliability of etchants 361 10.5. Etching and post-etching procedures 365

11. Etching techniques in applied research and development 368 11.1. Plastic deformation 368

11.1.1. Plastic deformation in terms of the dislocation mecha­nism 368

11.1.2. Dislocation rosettes 369 11.1.3. Some other phenomena related to slip and climb of

dislocations 370 11.2. Fracture, wear, sliding and dislocation damping 370 11.3. Revelation of defects, impurity distribution and microstruc-

tures 372 11.3.1. Structural characterization and origin of dislocations 372 11.3.2. Nature and character of dislocations 375

11.4. Surface preparation 375 11.5. Nature and depth of surface damage caused by mechanical

operations 376 11.6. Surface orientation 378 11.7. Chemical etching in semiconductor industry 379

11.7.1. Fabrication steps in a semiconductor device 379 11.7.2. Tapering of single and multiple dielectric layers 382 11.7.3. Etching profiles of semiconductor wafers 387 11.7.4. Etching profiles of semiconductor multilayers 396 11.7.5. Etch-stop techniques 402

404 Percentage composition of some liquid reagents fre­quently used in preparing etching and polishing solutions 405 Selective etchants for alkali halides 406 Selective etchants for insulators and dielectrics other than alkali halides 410 Dislocation etchants for metals and metallic alloys 420

Appendix Table A. 1.

Table A.2. Table A.3.

Table A.4.

XX Contents

Table A.5. Selective etchants for semiconductors 425 Table A.6. Polishing solutions for different types of crystals 434

References 440

List of symbols 463

List of abbreviations used 469

Author index 471

Subject index 489